Cremona's table of elliptic curves

8712 = 2³ · 3² · 11²

Field	Data	Notes
Atkin-Lehner	2- 3- 11-	Signs for the Atkin-Lehner involutions
Class	8712y	Isogeny class
Conductor	8712	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	23804337604608 = 211 · 38 · 116	Discriminant
Eigenvalues	2- 3-  2  0 11-  2  2  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-418539,-104219962]	[a1,a2,a3,a4,a6]
j	3065617154/9	j-invariant
L	3.0032095115882	L(r)(E,1)/r!
Ω	0.18770059447426	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	16	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	17424t5 69696cp6 2904d5 72a5	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 8712y5

a2	a3	a5	a7	a11	a13	a17	a19	a23	a29	a31	a37	a41	a43	a47	a53	a59	a61	a67	a71	a73	a79	a83	a89	a97
-	-	2	0	-	2	2	4	8	6	8	6	-6	-4	0	2	-4	2	-4	-8	-10	8	-4	6	2

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Quadratic twists for elliptic curve 8712y5

-4	8	-3	-11
17424t5	69696cp6	2904d5	72a5

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Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
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